Sounds like overactive letdown to me. I had the same problem my DS would cry so hard 'cause he was so frustratred! I was also drinking milk at the time (i also drank tons of it during pregnancy) but that was never the issue with me/him i still drink lots of milk no prob.
Try expressing some milk before nursing or pumping a bit, i found that helped.
And i don't think the acne is related, DS also had that and it started going away... I think it was about 6 weeks. I haven't changed my diet at all and he's happy as a clam so try the expressing first before cutting out dairy, i know i couldn't live without milk and cheeeeese~ good luck!